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<p>The most commonly used analytical delay models for signalised intersections, namely Webster’s or Ackelick’s, are based on the assumptions of random arrivals and deterministic discharge with one queue per lane. This may not be true under different traffic conditions. This study starts with checking these assumptions. Analysis of traffic patterns from a selected study site reveals that both arrivals and departures are random, prompting the use of an M/M/n queueing system for delay formulation. Based on this, a new analytical delay model rooted in queueing theory, designed to address the unique characteristics of multi-class and lane-free (MCLF) traffic, including multiple vehicle classes, lane-free movement, multiple number of servers, and arrival and service processes, is developed. The uniform delay is derived from the cumulative arrivals and departure curves, while the random delay term is by using the properties of the M/M/n queueing system. Empirical evaluations indicate that the proposed model significantly improves delay estimation, highlighting the critical need for developing delay models that are specifically adapted to traffic conditions.</p>

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A Stochastic Traffic Delay Model for a Multi-Channel Queuing System with Random Arrivals and Departures

  • 期刊论文

  • 发表日期：

    2026年3月30日

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  • Vinaya S. Mattungal,
  • Chithra A. Saikrishna,
  • Lelitha Devi Vanajakshi

摘要

The most commonly used analytical delay models for signalised intersections, namely Webster’s or Ackelick’s, are based on the assumptions of random arrivals and deterministic discharge with one queue per lane. This may not be true under different traffic conditions. This study starts with checking these assumptions. Analysis of traffic patterns from a selected study site reveals that both arrivals and departures are random, prompting the use of an M/M/n queueing system for delay formulation. Based on this, a new analytical delay model rooted in queueing theory, designed to address the unique characteristics of multi-class and lane-free (MCLF) traffic, including multiple vehicle classes, lane-free movement, multiple number of servers, and arrival and service processes, is developed. The uniform delay is derived from the cumulative arrivals and departure curves, while the random delay term is by using the properties of the M/M/n queueing system. Empirical evaluations indicate that the proposed model significantly improves delay estimation, highlighting the critical need for developing delay models that are specifically adapted to traffic conditions.